This project will address methodology development needs that are important for biomarker discovery. evaluation, and validation. These include: (i) analysis of structure and variance in functional data (spectra and/or images) for biomarker discovery;(ii) evaluating the predictive values of prognostic biomarkers;and (iii) development of group sequential study designs and analysis methods for biomarker validation. First, we focus on decomposing complex functional data via wavelet and/or differential analysis. This analysis of coherent structure and variation allows for a refined focus on features leading to discrimination between disease classes. Second, for evaluating the predictive values of prognostic biomarkers, we propose a simple yet clinically relevant measure, positive predictive value (PPV) curve for survival data. Estimating and inference procedures of the PPV curves, the use of PPV curves for comparing predictive values of biomarkers, selecting models, and combining biomarkers will be studied. A third aim is to develop group sequential study designs and analysis "methods for biomarker validation studies. Focus is on developing group sequential testing and estimation methods for biomarker validation studies but we will also investigate group sequential testing and estimation methods for prospective screening studies. The biomarker discovery, evaluation, and validation studies in the Early Detection Research Network (EDRN) provide the primary motivating settings for the proposed research.